Explicit solution of Riemann-Hilbert problems for the Ernst equation

Details Explicit solution of Riemann-Hilbert problems for the Ernst equation Explicit solution of Riemann-Hilbert problems for the Ernst equation

Jan 1998

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1998phrvd..57..857k&link_type=abstract

Physical Review D (Particles, Fields, Gravitation, and Cosmology), Volume 57, Issue 2, 15 January 1998, pp.857-862

Physics

6

Exact Solutions, Partial Differential Equations

Scientific paper

Riemann-Hilbert problems are an important solution technique for completely integrable differential equations. They are used to introduce a free function in the solutions which can be used at least in principle to solve initial or boundary value problems. But even if the initial or boundary data can be translated into a Riemann-Hilbert problem, it is in general impossible to obtain explicit solutions. In the case of the Ernst equation, however, this is possible for a large class because the matrix problem can be shown to be gauge equivalent to a scalar one on a hyperelliptic Riemann surface that can be solved in terms of theta functions. As an example we discuss the rigidly rotating dust disk.

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